ABSTRACT
Often, when we consider inhibition, there is a bias that the inhibitor is a substrate analog, but which will not actually undergo any catalysis to any product. Often, of course, that is true, such as when cyanide inhibits catalase, by serving as an analog to hydrogen peroxide and binding in its place at the active site. However, another molecule that certainly binds at the same location as the substrate is the product into which it is converted. Necessarily, the product must compete with the substrate for the active site. In the case of multiple substrates and multiple products, each product may compete against one or more substrates, depending upon the sequence in which each is bound and released. With two substrates resulting in two products, there are three possible scenarios, as determined by W. W. Cleland (1963a, b).
Ordered, Sequential Binding (see Figure 14.1): Both substrates A and B bind in order, are converted into products P and Q, which are released in order.
In this case, the substrate A and the product Q are both trying to bind to the same form of the enzyme. They will compete with one another, which means that as you increase the concentration of this product, the apparent value of Km for substrate A will increase. However, product P and substrate B are not trying to bind to the same form of the enzyme and will not be competitive to each other. Nor, for that matter, wlll product P compete with substrate A, nor will product Q compete with substrate B. If the biochemist observes a situation where only one substrate is competitive with only one product, it indicates that the enzyme proceeds in an ordered, sequential fashion, and it also identifies which substrate binds first and which product is released last.
If the pattern of binding is equilibrium ordered and sequential, then it can be observed on Lineweaver–Burke plots. It can also be described by a modification to the Michaelis–Menten equation:
https://www.w3.org/1998/Math/MathML"> v = V max [ A ] [ B ] ( K ia K b + K a [ B ] ) + ( 1 + [ I ] K i ) + K b [ A ] + [ A ] [ B ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429491269/91266b8d-9bd9-4768-abd3-c598bc3eb64f/content/TNF-CH014_eqn_0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
where Ka, Kb, and KI are the true Michaelis constants for A, B, and the inhibitor, respectively, and Kia is the apparent Michaelis constant for the inhibitor at the concentration of the substrate that is not being varied in the experiment.
Random: Substrate A and B can bind in any order and are converted into products P and Q, which can be released in any order, as diagrammed in Figure 14.2.
In this case, substrates A and B and also products P and Q are all capable of binding to the free enzyme. Because both products and substrates all bind to the same free enzyme form, E, both P and Q are competitive against both A and B. If the concentration of either is increased, they should increase the apparent Km of either substrate, without affecting v max. If this condition is observed, it often structurally corresponds to a binding pocket in which the substrates binds side-by-side. The identities of which substrate is designated “A” or “B” are not relevant, however, since either reactant could be considered “A” and either product could be considered “P”.
If the substrates and products bind in a random fashion, then the initial activity can be described by the following equation:
https://www.w3.org/1998/Math/MathML"> v = V max [ A ] [ B ] ( K ia K b ( 1 + [ I ] K i ) + K a [ B ] ) + K b [ A ] + [ A ] [ B ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429491269/91266b8d-9bd9-4768-abd3-c598bc3eb64f/content/TNF-CH014_eqn_0002.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
Ping-Pong: As shown in Figure 14.3, substrate A binds, is catalyzed, and modifies the enzyme to form “F”. Product P is released. Enzyme form “F” binds substrate B, and transfers its modification onto product Q, restoring itself to form “E” in the process.
In this case, product Q and substrate A bind to the E form of the enzyme, while product B and substrate B bind to the F form. Therefore, Q will compete with A, but will not compete with B. At the same time, P will compete with B but not A. It is not possible to designate with complete certainty which substrate is the true “A” and which the true “B”, but it is possible, having arbitrarily designated one of the substrates “A” to assign the identities of everything else. Whenever one product is competitive to one substrate and the other product is competitive to the other substrate, the enzyme is always operating in a ping-pong fashion. Many enzymes that transfer phosphate groups will display ping-pong behavior.
The rate equation is more complicated when ping-pong behavior is observed:
https://www.w3.org/1998/Math/MathML"> v = V max [ A ] [ B ] ( K ia K b + K a [ B ] ) ( 1 + [ I ] K i1 ) + K b [ A ] + [ A ] [ B ] ( 1 + [ I ] K i2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429491269/91266b8d-9bd9-4768-abd3-c598bc3eb64f/content/TNF-CH014_eqn_0003.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
where Ki1 and Ki2 are the two potential equilibria for binding either to the E or F forms of the enzyme. In many cases, binding affinity for one enzyme form or the other is so weak that the other equilibrium may be ignored. This is not always the case, however.
The binding and release scheme for ordered, sequential bimolecular kinetics. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429491269/91266b8d-9bd9-4768-abd3-c598bc3eb64f/content/fig14_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> The binding and release scheme for random bimolecular kinetics. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429491269/91266b8d-9bd9-4768-abd3-c598bc3eb64f/content/fig14_2_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> The binding and release scheme for ping-pong bimolecular kinetics. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429491269/91266b8d-9bd9-4768-abd3-c598bc3eb64f/content/fig14_3_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>